a neural network approach to the steel surface wear on

JurnalTribologi 22 (2019) 74-107

Received 27 September 2018; received in revised form 2 January 2019; accepted 23 January 2019. To cite this article: Capitanu et al. (2019). A neural network approach to the steel surface wear on linear dry contact, plastic material reinforced with SGF/steel. JurnalTribologi 22, pp.74-107.

© 2019 Malaysian Tribology Society (MYTRIBOS). All rights reserved.

A neural network approach to the steel surface wear on linear dry contact, plastic material reinforced with SGF/steel Lucian Capitanu 1, Victor Vladareanu 1, Luige Vladareanu 1, Liliana-Laura Badita 2,*

1 Institute of Solid Mechanics of the Romanian Academy, 010141 Bucharest, ROMANIA. 2 National Institute of Research and Development in Mechatronics & Measurement Technique, 021631 Bucharest, ROMANIA. *Corresponding author: [email protected]

KEYWORDS ABSTRACT

Plastics with SGF Steel wear Friction coefficient Contact temperature ANN

The aim of the paper is to approach the study of wear on a metallic surface in the case of dry linear contact, plastic material reinforced with short glass fibres (SGF) on surfaces of C120 and Rp3 steel, through the method of artificial neural networks (ANN). This is because wear processes involve very complex and powerfully nonlinear phenomena. Consequently, analytic models are difficult or impossible to obtain. This is also necessary due to the multiple inputs (normal load – contact pressure, relative sliding speed, measured contact temperature, materials properties) and outputs (width and depth of the wear scar, measured contact temperature) which influence each other continually. A multitude of experimental tests was performed with different loads and speeds, which have led to some conclusive results but, in some cases, with relatively high variance. Therefore, the paper aims to use the same experimental data in an ANN – based approach, which is a state-of-the-art modelling method, due to its properties for learning, generalisation and nonlinear behaviour, adequate to plastic materials armed with short glass fibres. The innovative approach is compared with a baseline model featuring multivariate linear regression optimised using gradient descent.


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1.0 INTRODUCTION In wear processes, similarly to fabrication processes, very complex and nonlinear phenomena

are involved. Consequently, analytical models are difficult or impossible to come by. However, improvements in the performance and reliability of mechanical equipment and production instruments require a precise modelling and prediction of the wear phenomenon. To this end, artificial neural networks (ANNs) possess a series of desirable properties for modelling systems and processes: the ability to approximate universal functions, learning from experimental data, high tolerance for lacking or noisy data and good capacity for generalisation. In tribological applications two main functions of ANNs are particularly useful:

- continuous approximation of a multivariable function, used for modelling processes; - classification, meaning a discrete approximation of functions, used for recognising the

functioning conditions of machines. The former can be obtained through feed-forward neural networks (NNs, named Multi-Layer

Perceptrons - MLPs), which can be obtained using the NN self-organisers, like the Kohonen theory and the adaptive resonance theory (ART). Equally, MLP can be used for classification if a supplementary discriminator for the output values is added. Both functions are already applied in the field of tribology and machines and presented in various recent papers.

The paper presents the approach to modelling a dependency between the various variables of interest involved in the friction process, using advanced statistical and optimisation algorithms on a dataset obtained from hardware simulation. The subject draws a growing interest from the research community with the advent of highly advanced, intelligent classification, optimisation and regression algorithms. Similar directions were investigated in Zhang et al., (2003), Panda et al., (2006) and Flepp et al., (1999), as regards the potential of supervised or unsupervised learning and modelling the results of friction, while surveys such as Ripa and Frangu (2004) deal with the various possibilities for undertaking this task. Lastly, the paper builds upon previous work done by Rus et al., (2014), Vladareanu et al., (2018). The importance of the subject matter is illustrated by its use in building artificial joints and prosthesis among others – Capitanu et al., (2008), Al-Zubaidi et al., (2013).

The state of the art includes many papers that broach the usefulness of ANNs in investigating tribological phenomena. Thus, Al-Zubaidi et al. (2013) specifies that the surface roughness is considered the quality index of machine parts. There have been used a number of different techniques for modelling metal cutting processes. Previous studies have shown that artificial intelligence techniques are new calculation methods that provide solutions for nonlinear and complex problems such as metal cutting processes. The authors have used an adaptive inference neuro-fuzzy system to predict the roughness of a surface after Ti6Al4V milling with covered (PVD) and uncovered cutting tools, under dry cutting conditions. The real experimental results have been used for training and testing the adaptive neuro-fuzzy inference system (ANFIS) models, and the best model was selected based on the least mean square error. A generalised bell-shaped function was adopted as a membership function for the modelling process. The conclusions provided proof of the ability of ANFIS to model surface roughness in the final milling process and to obtain a good fit between the experimental and predicted results.

Sudarshanet et al., (2014) presented an artificial neural approach “for predicting the abrasive behaviour of epoxy composite reinforced with carbon fibre. Artificial neural networks have emerged as a good candidate in mathematical models of wear, due to their ability to deal with nonlinear behaviour, learning from generalization and experimental data”. In this paper the authors are investigating the potential use of neural networks for predicting abrasive wear


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properties of epoxy composite unreinforced and reinforced with graphite fibres in different test conditions. An inverse propagation neural network was used, with the 3-5-1 architecture, to predict weight loss in the abrasive wear simulation. The network performance of different training algorithms is evaluated using the coefficient of determination B, the sum of the mean square errors, the mean relative error, the mean square regression error, as a measure of quality. The results show that the performance of the training logarithm Levenberg-Marquardt (LM) is superior to all other algorithms. Finally, a well optimized and trained neural network with LM algorithms is used, that predict wear properties as a function of test conditions, in accordance with input data sets. The results show that the predicted data are perfectly acceptable as compared with the actual results of experimental tests. Therefore, it is expected that a system of well-trained artificial neural network to be useful in predicting the weight loss in complex abrasive wear situations with three bodies of polymer composites.

Friedrich K., et al., (2018) reported on the wear performance of dry and oil-impregnated palm wood. It was first investigated the sliding wear of dry fiber palm wood in dry conditions against polished steel. The tests were carried out in two different configurations, i.e. pin on disk and ring to plate. In both cases, the transverse orientation in the fiber plane led to the highest values of the friction coefficient and the specific wear rate. The normal and parallel fiber orientations have shown better performance. In all cases, the friction coefficient was quite high (average range between 0.4 and 0.7), while the specific wear rates varied between 10-6 and 10-5 (mm3/Nm). The latter are comparable to those of short fiber reinforced thermoplastics. Impregnation in different oils has reduced wear rates and friction coefficients have been reduced to values ranging from 0.1 to 0.3.

Shebani and Pislaru (2015) noted that measuring and modelling wear are fundamental problems in the industrial field, mainly related to economy and safety. Therefore, a study of measurement and estimation of wear is needed. The test commonly used to study the wear performance is the pin-on-disk test. In this paper, the pin-on-disk test was used to investigate the effects of normal load and the material hardness on the wear in dry sliding conditions. In the pin-on-disk device, two samples were used: one is a pin with a tip, which is made of steel and is positioned perpendicular to the second sample, a disk made of aluminium. The wear of the pin and the wear of the disk were measured using the following instruments: Talysurf, a digital microscope and instrument "alicona" - a 3D micro coordinate measurement device (Infinite Focus). The Talysurf Taylor Hobson profilometer was used to measure the depth of pin / disk wear, the digital microscope to measure the diameter and width of the wear scar, and alicona was used to measure the wear of the pin and the disk. Thereafter, the Archard model was used, ASTM and neural network model, for modelling the pin / disk wear.

Jumahat A., et al., (2015), analysed the wear properties of nanosilica filled epoxy polymers and FRP composites. They used the glass fibers as reinforcement material. The fibers were mixed with three different percentages of epoxy modified nanoparticle resin, i.e. 5% by weight; 13% by weight and 25% by weight, for the manufacture of the desired FRP composites. The nanosilica effect on wear properties was evaluated using dry wear and suspension tests. The results show that increasing the amount of nanosilica content reduced the amount of accumulated mass loss. FRP laminates with 25% nanosilicate by weight have been found to have the highest wear resistance. Nanosilicafiber reinforced polymeric composites have a high potential in tribological applications, such as ball bearings and snowmobiles.

Pati and Satapathy, (2013) studied the furnace dross, LD (Linz-Donawitz), which is a major solid waste generated during the manufacture of steel in huge quantities. It comes from dross


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formers such as lime / burnt dolomite and oxidation of silicon, iron, etc., during refining the iron steel in LD furnace. Although they have been suggested several ways of use, it has not been yet explored as filler in polymer matrices. The authors prepared five different compositions (0, 7.5, 15, 22.5 and 30 wt% dross LD) for reinforcing the epoxy resin, by simple manual filling technique. There have been made studies of erosion of the solid particles, in accordance with ASTM G-76 testing standards, following a well-planned experimental program, based on the Taguchi experiments design. An erosion testing device of air jet type was used, capable of producing reproducible erosive wear situations. For erosion, it uses dry sand of different sizes. Significant parameters of the process are identified that mainly influences erosion rate. In order to minimize the erosion rate, the impact velocity, the content of LD, the thrust angle and the temperature of erosion in descending sequence are considered as significant factors. There is put forward for consideration a predictive model based on a neural artificial network to predict erosion performance composites in a wide range of conditions of erosive wear. This model is based on data obtained from experiments and protocols involving training, testing and prediction. This paper shows that the ANN model helps to save time and resources that are required for a large number of experimental studies and successfully predicting erosion rate composites, both inside and outside the experimental area. This work also shows that LD dross, despite the fact that it is a waste, has reinforcement features of good quality, because it improves the resistance to erosion of the polymer resin.

Martini Mohmad at al., (2018) reported on physical-mechanical properties of palm kernel activated carbon reinforced polymeric composite: Potential as a self-lubricating material. Activated carbon from the palm kernel is one of the potential autolubricant materials. Therefore, this study investigated the effect of activated carbon composition of palm oil on the physico-mechanical properties of the palm kernel activated carbon composite. The polymer resin was reinforced with 65%, 70% and 75% by weight activated carbon and compacted in a mould at 70°C, with a pressure of 20 tonnes for 15 minutes by the compaction technique. Samples were prepared for traction, hardness, porosity, density and water absorption tests. The 65% sample had the best hardness properties and had the lowest density but not the traction test, compared to the other two samples. Also, this sample has proven superiority in hardness and density compared to other natural synthetic polymer composites.

Analysing the surveillance of the intelligent tool, turning at high speed titanium alloy Ti-6Al-4V, Fadare et al., (2009), showed that intelligent monitoring of working conditions of a tool is an essential requirement for automatic processing unit operations. To this end, the authors created a model of Multi-Layered Perceptron (MLP) neural network to monitor online conditions for tool wearing rapid turning titanium alloy (Ti-6Al-4V). The manufacture processes were performed for typical gross and fine operations with a cutting speed of (90 - 120 m / min), feed rate (0.15 - 0.2 mm / rev) and cut depth of (0.5 - 2.0 mm) using uncoated cemented carbide (grade K10) with the ISO name "CNMG 120 412". At each manufacture operation were measured the maximum wear at tool flank (VBmax), cutting forces (advance force Fx, and tangential force, Fz) and the motor shaft power. Cutting parameters (cutting speed, feed rate and cutting depth), the cutting force and the power of the shaft have been used separately or in combination, as a set of input data in the neural network, to predict wear of the cutting tool at various stages of propagation wear (light, medium and heavy). The neural network model was designed using neural MATLAB toolbox. The authors of the present paper evaluated the model accuracy to predict tool wear at different stages of wear, on the basis of percentage error (PE), for operations both gross and finishing. The results showed that the phase of gross wear (PE = ± 5%) was predicted more accurately as compared


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with the stages of light wear (PE = + 5 to - 10%) and medium (PE = + 25 to - 30%). The combination of power, power signals and cutting parameters improved the model performance.

R.M. Nasir and N.M. Ghazali (2014) reported on the tribological performance of paddy reinforced polypropylene (PSRP) and unidirectional glass-pultruded-kenaf (UGPK) composites. In the standard preparation and manufacture of incorporated natural fiber composites, 5% by weight of natural fibers is sufficient to be stiffened and homogenized in the parent matrix because it has been found that the mechanical strength increases by more than 25% relative to the pure matrix. Therefore, paddy straw and kenaf were potentially candidates in the northern Malaysia because of their abundance and ease of completion. A one-way glass pultrued-kenaf polypropylene (UGPK) and straw reinforced polypropylene (PSPP) was studied, focusing on its tribological performance. At the same time, the friction and wear properties were examined using the pin on disk machine at ambient temperature under dry contact conditions. The tests were performed at different sliding speeds (1.178-2.749 m/s) and normal loads (9.82-19.64 N). The results showed that the specific wear rate and friction coefficient decreased with the increase in normal applied load and sliding speed, but the normal load applied was more important. The friction coefficient varies from 0.5 to 4 and the wear rate varies from 0.5 to 4 x 10-5 mm3/Nm for PSRP. The friction coefficient of UGPK is in the range of 2.76 to 4.54 at the test parameters given, while the wear rate varies between 0.8 and 1.79 × 10-5mm3/ Nm. The failure mode observed during the test was micro-buckling and was followed by splitting while an interfacial fiber - matrix failure occurred.

Shukla (2006) reported an overview on applications of artificial neural networks in the processing domain. The property of learning and nonlinear behaviour make them useful for complex nonlinear process modelling, better than analytical methods. They are useful in some specific points in the field: processes and wear particles, manufacturing, friction parameters, defects in mechanical structures. The results obtained by the authors are described in their interdisciplinary research, proving that neural network is a useful tool in the design phase, as well as the stage of running or operating.

Rao et al. (2012) worked with the rolling element bearings, which are widely used in almost all global industries. Any critical failure of these important components would not only affect overall system performance, but also reliability, safety, availability and their profitability. Their proactive strategy is to minimize imminent failures in real time and at minimal cost. Innovative developments are recorded in the technology of artificial neural networks (ANN).

Research and significant developments are of interest in many universities, private and public organizations and an impressive published literature is available which highlights the potential benefits of ANNs and intelligent control interfaces involvement in smart monitoring, diagnosis, prognosis and management of real time control systems with applicability to the surface wear control systems developed by Vladareanu et al., (2009, 2010), or using a versatile intelligent portable platform by Vladareanu et al., (2015, 2017).The paper tries to critically analyse recent trends in this area of interest.

Chen and Savage (2001) describe an approach to fuzzy networks for a recognition system of multilevel surface roughness (FN-M-ISRR), whose aim is to predict the surface roughness (Ra) under multiple cutting condition, determined by the material of the tool, the tool size, etc. The surface roughness was measured indirectly by extrapolation of vibration signal data and the cutting conditions, which have been collected in real time by an accelerometric sensor. The data were analysed and a model was built using a neural fuzzy system. The experimental results have shown that the parameters of the cutting speed, the advance made by tool, the depth of the cut


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and variable vibration can predict the surface roughness (Ra) in eight different combinations of features of the tool and the work piece. Neural fuzzy system is presented to predict the surface roughness (Ra) during a milling operation, with a 90% accuracy of prediction.

Kalidass et al. (2012) showed that tool wear prediction plays an important role in productivity and better-quality products. Their work focuses on two regression neural mathematical models (ANN) for the prediction of tool wear. In the paper the response variable (output) is taken as the measured flank wear during milling, while the helical angle, spindle speed, feed rate and depth of cut are taken as input parameters. Design of experimental techniques (DOE) has been developed for four to five levels factors for the experiments. Experiments were carried out to measure tool wear by the technique based on the DOE in a vertical machining centre, the AISI 304 stainless steel, using a cutting tool with a solid carbide fine core. The experimental values are used in Six Sigma software development to find coefficients of the regression model. Experimentally measured values are also used to train the regression propagation neural networks (ANN) for the prediction of tool wear. Expected values of the response to both models, the regression and ANN are compared to the experimental values. It was found that the neural network predictive model is able to better predict the tool flank wear prepared interval.

Molinero Velasco (2012) shows that the telecommunication networks enclose items of very different types working together to provide services. Quite often, hardware failures are interrelated and it is difficult for specialized technicians in specific hardware to find these relationships. In this context, Bayesian Networks (BN) offers a flexible solution because they allow modelling causal relationships between element failures and deduction from the existing evidence. The aim is that network technicians be informed about the real reason for the existence of probable failures and problems, optimizing resources and reducing recovery time. In addition, this approach can build a hierarchy of real elements, allowing the discovery of hidden dependencies between elements. The result of this work was to develop an attached module to an incident management system (trouble ticketing system, TT).

McLeay and Turner (2011) shows that high costs of qualified operators in the production processes have created a demand of diverting the staff that engaged with lamps manufacture. Process monitoring systems have become a rising researched field in recent years because it requires intelligent systems to replace manual intervention in existing processes. In addition, by using sensors and modern techniques in signal processing, monitoring systems can get more information about a process and therefore can further reduce costs, although the maximum life span of cutting tools, cutting parameters and the remains of material used in reprocessing. With many areas of application available, such as monitoring working conditions, avoiding overexertion or feedback control of cutting parameters is not always obvious as key issues that need an intelligent monitoring. In addition, various manufacturing processes have different monitoring requirements and limitations. This paper examines an analytical approach to define the requirements of a monitoring system. To determine the shortcomings of current production processes, the authors of the present paper carry out an analysis of the failure process (Failure Mode Effect Analysis - FMEA). From this analysis can be used relationships between failures, causes and effects to superimpose conditional relations between process defects and features of the sensor signal in a monitoring system.

Wang and Chan (2012) present a new technique for monitoring a manufacturing facility by observing movement characteristics as components of the system. Most modern monitoring systems are based on different sensory devices for capturing information about production, but the proposed methodology requires only simple counters in combination with a mathematical


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model. In the proposed technique, a turbine will be segmented in regions of interest ROI, and the lock process in a turbine can be seen following each ROI. More importantly, an implementation algorithm was developed for counters subjected to a maximum time for defined response and for system design purposes.

Mak and Nitin (2014) discuss the adoption of selective automation or automation as a solution to most problems of productivity in the hard disk industry (HDD), as the industry continues to grow at an annual growth rate of 40%. An automated production line was developed for the manufacture of a rake head assembly (head gimbal assembly - HGA) as part of the automation solution. In the automatic production line of the HGA, a soldering station using the solder ball jet method (jet solder ball - SJB) connects the circuit suspension to the slider body. The authors proposed a Bayesian approach to automatic optical inspection (AOI) of connecting SJB in the HGA, implementing Tree Enhanced Naive Bayes Network (TAN-BN) plus the classifier to check in-situ, using Genie / SMILE in the software inspection. The system is improved with the results of the control, reaching a total accuracy of 91.52% with 660 parts produced in a blind test.

Feng et al. (2002) show that the selection and validation of models is essential to judge the performance of manufacturing processes. Proper selection of variables minimizes the mismatch error of the model, while selecting appropriate models, reduce estimation error of the model. The models are validated to minimize the model error of prediction. The paper proposes a cross-validation procedure for the selection and predictive regression of neural network models. They analyse the impact specifications and tolerances of surface roughness on the turbine manufacturing processes and product quality differentiation and finally, product cost and time of execution. Using experimental data from a study of roughness from a turned surface to demonstrate concepts developed with regression techniques and neural network used rather than descriptive for predictive modelling purposes. For decades, the arithmetic mean (Ra) and the sum of the square roots (Rq) were the two major measures of surface roughness to define a wide range of surfaces for mechanical product. In recent years a number of disadvantages have been identified with the above measures. To map more closely and as rigorously scientific possible and closely to the roughness of the functions and performance of the product, ISO13565 defined a different set of measurements, including Rk, Rpk, Rvk, Mr1 and Mr2. This not only made the planning process different and much more difficult, but also made the modelling of a relationship between these measures of roughness and machining parameters a problem of multiple input and multiple output.

Flepp (1999) in his PhD thesis entitled "Diagnosis of wear in mechanical seals neural network" provides an introduction to technical diagnosis and describes the main techniques that apply today. These methods are then compared to the advantages of neural networks in solving diagnostics. Moreover, the process of wear for seals of large mechanical pumps is explained using neural networks. Neural network capabilities depend to a large extent on the quantity of forming substance and the data set. It is therefore important to have significant training data in large numbers and small values.

Liu et al. (2014) showed that due to the highly geometric accuracy and surface finish for many modern products, during manufacturing processes have been used correcting processes. However, it is also well accepted that correction is one of the most complicated manufacturing processes due to high nonlinearities, uncertainties and intrinsic characteristics that vary over time. There are many challenging problems in the process, limiting the practice quality and global production. With growing demands for geometry precision of parts, a better surface integrity, higher productivity and other parameters requested for the product (e.g. minimizing micro-


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damage below the surface), with a reduced operator intervention were studied and different control methods implemented to control the position, speed, force, power, temperature, and rate of material removed (Material Removal Rate - MRR) during the process of grinding to achieve the desired performance of the system as regards cost and time. This paper examines the different control strategies to provide guidance for researchers and industry practitioners to improve final product quality, with an improved flexibility of the process.

Abouelatta (2013) refers in his paper to the prediction of processing and the surface roughness using artificial neural networks. The surface roughness is considered one of the specified customer requirements in processing. For the efficient use of machine-tools, it is necessary to select the manufacturing process and determine the optimum cutting parameters (speed, feed and depth of cut). It is therefore necessary to find a suitable way to select and find an optimum machining process and cutting parameters for a specified amount of surface roughness. In this paper, the processing was carried out on AISI 1040 Steel using dry cutting state in a lathe, milling machine and grinding, and then the surface roughness was measured. There were forty-five experiments performed using speed, cutting feed and depth of the variable to find the surface roughness parameters. The data was randomly divided into two sets: 36 training data sets and 9 sets of test data. Training data set was used to train various models of neural networks (ANN) to predict processing and surface roughness parameter values through the network of reversed propagation. The experimental data collected from tests were used as input parameters of a neural network, to identify the sensitivity during processing operations, cutting parameters and surface roughness. The selected indicators were used to design a suitable algorithm for the prediction of the manufacturing processes. A software algorithm was developed and implemented to predict processing and surface roughness values. The results show that the proposed models are capable of predicting the processing operations, cutting parameters and surface roughness.

Ripa and Frangu (2004) have shown the potential of artificial neural networks in the wear and manufacturing processes. Their properties of learning and the nonlinear behaviour make them useful for further modelling of nonlinear complex processes, compared to analytical methods. Neural structures are shown, which are considered suitable for such designs. Applications found in reference documents consist mainly in prediction and classification. They have several things in common, specific for the industry: processes and wear particles, manufacturing, friction parameters, defects in mechanical structures. It describes the results obtained by the authors quoted in the interdisciplinary research, proving neural network is a useful tool in the design phase and stage of operation or functioning.

In a different paper, Zhang et al. (2003) analysed the artificial neural network prediction of erosion wear of the polymer. They achieve an erosive wear of three polymers, namely polyethylene (PE), polyurethane (PUR) and an epoxide of hydrothermal decomposed modified polyurethane (PUR EP-hydrothermally polyurethane decomposed). Three independent sets of measurement data were used and the characteristic properties of erosive wear of these polymers to prepare and test the neural networks were explored. For the first two examples of materials, the angle of impact of solid particle erosion and some characteristic properties were selected as input variables of the ANN. As for the third, the material composition, i.e. the weight content HD epoxy and PUR, also have been implicated as additional input variables of the ANN. In all these cases, the output parameter was the speed of erosive wear. Acceptable ANN predictive qualities were achieved, demonstrating that about35-80% of the test data set chosen randomly has a coefficient of determination for these three cases B ≥ 0.9. The classification of characteristic


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importance properties such as erosive wear rates could provide some information about which properties have a stronger relationship with wear, for each polymer. Although the ANN approach is only a phenomenological method, it is believed that a well created ANN is also helpful for understanding the mechanical problem considered.

The present work is aimed at the treatment using the method ANN of experimental results obtained by the authors of this in the analysis of linear dry contact of polymer reinforced with short glass fibres (SGF) on the surface of the two-alloy steel hardened, C120 - a injection mould steel with 59 HRC hardness and Rp3 - a tool steel of 62 HRC hardness.

Wear performance of the two steel alloys, C120 and Rp3 has been previously studied in the case of linear dry contact with each polymer (polyamide and polycarbonate) reinforced with different percentages of short glass fibres (SGF) – (Capitanu et al., 2014). Studies have shown a strongly nonlinear variation in friction coefficient, wear, and contact temperature (output parameters), depending on the normal load applied, the relative sliding speed and the characteristics of the material in contact (input parameters). 2.0 EXPERIMENTAL PROCEDURE

Experimental studies were made on a universal tribometer, Fig. 1.

(a)

(b)

Figure 1: Overview of the tribometer (a), and a schematic of its representation (b): (1) – cylindrical liner, (2) - plane disk sample, (3) – nut, (4) – driving shaft, (5)- hole, (6) - trapezoidal transmission belts, (7) – electric engine, (8) – calibrated spring system, (9) – thermocouple, (10) – tank, (11) – base, (12) - tube.


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The universal tribometer allows the study of several types of friction couples with different contacts - on the surface (pin on flat), linear (liner on flat), point (spherical thimble on flat), etc. The experimental studies presented in this paper were conducted on a linear contact couple (polymer with SGF thimble/ steel flat disk). Figure 1 shows an overview of the universal tribometer (a) with the experimental linear contact module on the top right, and a schematic representation of this module (b).

The friction couple is built out of a cylindrical liner (1) and a plane disk type sample (2). The liner is fixed with the help of a nut (3) on the driving shaft (4), and the disk sample is placed in a special hole made within the elastic blade (5). The disk sample was built in such a manner so that the base allows the disk to make small rotations around the edge of a knife fixed in their holder, perpendicularly on the driving shaft. In this way a uniform repartition of the load on the entire linear contact between the liner and the disk steel sample is ensured, even if there are small building or assembling imperfections. An electric engine (7) puts the rod (4) into a rotation movement using trapezoidal transmission belts (6).

The experimental device allows to simultaneously measure the normal and tangential (friction) efforts through resistive converter strain-gauges, assembled on the elastic blade (5). The use of a pair of converters strain-gauges connected within the circuits of two strain-gauges bridges, offers the possibility to make simultaneous measurements, while separately, gives the possibility to measure the normal and friction forces. The normal load is applied to the elastic blade (5), through a calibrated spring system (8). The installation allows to register the friction force on an X-Y recorder. The tests’ duration is controlled through an alarm clock and the contact temperature is measured with the help of a miniature thermocouple (9), connected to a millivoltmeter calibrated in 0C. The installation offers the possibility to study the wear behaviour by using also several other radiometers technics. For this purpose, the installation includes a tank (10) assembled on a base (11) and a tube collecting the radioactive wear particles (12). 2.1 Analytical Approach to Metal Surface Wear

The operation under the load of the friction couple with linear contact, situated under the load and in the presence of relative sliding motion of the plastic thimble reinforced with fibre glass, on the surface of the sample steel, highlights the appearance of a scar wear on the flat surface of the metal, whose shape is schematically shown in Figures 2(a) and (b).

The wear trace occurs by penetration of the cylindrical thimble, under the influence of the normal load, in the plane semi-coupled material. In theory, the holding thimble is considered as rigid and relatively small in view of the backside imprint, so it can be considered as made up of a sum of cylinder areas of the length equal to p.

The radius r can’t be found in the couplers plastic / metal, with the radius of the cylindrical thimble. This is due to elastic deformation of the thimble under load, which aims at increasing its radius in the contact area. This is illustrated schematically in Figure 2(b).

Noting the non-deformed sleeve radius r1 and the radius r2 - deformed under load, shown in Figure 2(b), that r2 > r1. There were considered the following three polymers:

A. Nylonplast AVE Polyamide + 30% glass fibres; E2A = 40.25 MPa. B. Noryl Polyamide + 20% glass fibres; E2B = 31.76 MPa. C. Lexan Polycarbonate + 20% glass fibres; E2C = 42.08 MPa.


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(a)

(b)

Figure 2: The appearance of wear scar on the surface (a). Applying the analytical method used in calculating the volume of material and (b) the elastic deformation of the cylindrical thimble in the contact area, in a - theoretical case, and b - real case. Adapted from (Rus et al., 2014).

The imposed condition has allowed to establish the following values of the maximum contact pressure of the dry linear couplings contact, in the case of three plastic materials (A, B, C) reinforced with SGF, the 5 normal loads (contact pressures), indexes 1 to 5 of notations of the pressures that have been subjected to, for each of the 7 relative sliding speeds used (18.56; 27.85; 37.13;46.41; 55.70; 111.4 and 153.57 cm/s):

pA1 = 16.3 MPa; pA2 = 23.5 MPa; pA3 = 28.2 MPa; pA4 = 32.6 MPa; pA5 = 36.4 MPa; pB1 = 12.3 MPa; pB2 = 17.4 MPa; pB3 = 21.4 MPa; pB4 = 24.6 MPa; pB5 = 27.6 MPa; pC1 = 16.9 MPa; pC2 = 23.9 MPa: pC3 = 29.3 MPa; pC4 = 33.8 MPa; pC5 = 37.8 MPa.

After inspection and measuring the wear scars of metal surfaces, the widths of each wear scar

were measured, their volume was calculated (the amount of material lost through wear) and were traced their variation curves depending on applied load (contact pressure), the relative speed of


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sliding contact with the temperature specification of the optical image and presentation of the scar. This quantitative-qualitative assessment method was submitted, in Rus et al., (2014). All tests took place for 60 minutes, so that the calculated wear volumes are actually wear rates.

2.2 Results of The Analytical Approach to Metal Surface Wear

Numerical values were determined by the elasticity modules listed above, and the deformed thimble radii (r2) according to the Eq. (1), imposing pmax is provided as 𝑝𝑚𝑎𝑥 < 0.5 𝐻, where H is the Brinell hardness for the plastic thimble is enough so it will not be crushed.

h ≈ l2/ 8r2 (1)

A part of the experimental data is shown in Tabs. 1-16.

Table 1: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Nylonplast AVE Polyamide+ 30% SGF / C120steel at a sliding speed of 18.56 cm/s.

N (N)

Friction coefficient μ

Contact temperature T (0C)

lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)

Mean wear rate hmu (10-4 mm/h)

Vmu (10-6 cm3 /h)

10 0.3 108 0.090 0.9316 1.365 0.9649

0.1384 10 0.096 0.9982 1.410

20 0.39 140 0.232 2.4409 4.386 2.4798

0.4404 20 0.239 2.5187 4.423

30 0.4 150 0.418 4.4392 8.804 4.0336

0.8381 30 0.345 3.6281 7.958

40 0.43 165 0.490 5.1708 12.743 5.4874 1.3086 40 0.488 5.1708 12.743

Table 2: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Nylonplast AVE Polyamide + 30% SGF / C120 steel at a sliding speed of27.85 cm/s.

N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

10 0.32 135 0.272 2.9538 2.366 2.9149 0.2352 10 0.265 2.8760 2.339 20 0.4 150 0.352 3.7743 5.388 3.7076 0.5338 20 0.540 3.6409 5.288 30 0.43 175 0.469 5.0059 9.226 4.6726 0.9015 30 0.409 4.3392 8.694 40 0.49 190 0.579 6.1597 13.832 6.1374 1.3796 40 0.49 190 0.579 6.1597 13.832


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Table 3: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Polyamide + 30% SGF Nylonplast AVE / C120 steel at a sliding speed of 37.13 cm/s.

N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

10 0.38 150 0.257 2.7871 2.4524 3.6871 0.2999 10 0.419 4.5871 3.5475 20 0.40 160 0.364 3.9076 5.4873 4.1909 0.5674 20 0.415 4.4743 5.8604 30 0.43 175 0.456 4.8614 9.1728 5.1336 0.9418 30 0.500 5.4059 9.6642 40 0.5 190 0.592 6.3041 13.887 6.7152 1.4269 40 190 0.565 7.1264 14.651

Table 4: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Polyamide + 30% SGF Nylonplast AVE /C120 steel at a sliding speed of 46.41 cm/s.

N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

10 0.27 150 0.363 3.9649 2.7391 3.8871 0.2714 10 0.349 3.8093 2.6890 20 0.28 155 0.423 4.5612 5.8694 4.4243 0.3792 20 0.398 4.2854 5.7188 30 0.30 180 0.573 5.9281 10.128 5.7447 0.8606 30 0.519 5.5614 7.0842 40 0.33 220 0.805 8.6708 16.307 8.5486 1.6207 40 0.783 8.4264 16.107


N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

10 0.28 150 0.416 4.5538 2.9484 4.4704 0.2914 10 0.401 4.3871 2.8801 20 0.29 200 0.454 4.9076 6.1242 5.6298 0.3792 20 0.584 6.3520 6.8524 30 0.31 180 0.695 7.5170 11.384 7.5505 1.1404 30 0.701 7.5836 11.423


87


N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

10 0.32 250 0.449 4.9204 2.5935 4.9482 0.2830 10 0.454 4.9760 3.0667 20 0.42 280 0.563 6.1187 6.8341 5.9409 0.6734 20 0.584 6.3520 6.8524 30 0.49 293 0.740 8.0170 11.739 8.0003 1.1732 30 0.737 7.9536 11.723

Table 7: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Polyamide + 30% SGF Nylonplast AVE / C120 steel at a sliding speed of 153.55cm/s.

N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

10 0.34 260 0.419 4.1538 2.5935 5.1760 0.3101 10 0.466 6.1982 3.0667 20 0.41 280 0.593 6.4409 6.8341 6.4742 0.7021 20 0.598 6.5076 6.8524 30 0.48 292 0.785 9.0281 11.739 9.0170 1.2435 30 0.834 9.0059 12. 514

Table 8: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Polyamide + 30% SGF Nylonplast AVE / Rp3 steel at a sliding speed of 18.56 cm/s.

N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

10 0.29 98 0.217 2.3427 2.1203 2.3815 0.2136 10 0.224 2.4204 2.1521 20 0.29 100 0.258 2.7298 4.4681 2.7798 0.4573 20 0.267 2.8298 4.6774 30 0.31 120 0.305 3.1836 7.5484 3.2392 0.7610 30 0.737 7.9536 11.723 40 0.4 155 0.379 3.9375 11.211

3.9708 1.1247 40 0.385 4.0041 11.284


88


N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

20 0.37 225 0.322 3.4409 5.1597 3.4464 0.5164 20 0.323 3.4520 5.1688 30 0.41 275 0.361 3.8059 8.1900 3.7670 0.8149 30 0.354 3.7281 8.1081 40 0.43 300 0.401 4.1819 11.521

4.6541 1.2094 40 0.486 5.1264 12.667

Table10: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Polyamide + 30% SGF Nylonplast AVE / Rp3 steel at a sliding speed of37.13 cm/s.

N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

20 0.28 150 0.397 4.2743 5.7330 4.1076 0.5619 20 0.367 3.9409 5.5054 30 0.33 205 0.423 4.4948 8.8725 4.2392 0.8627 30 0.377 3.9836 8.3811 40 0.39 250 0.474 4.9930 12.522

5.0041 1.2531 40 0.476 5.0152 12.540


N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

20 0.28 150 0.409 4.4076 5.8240 4.5242 0.5833 20 0.430 4.6409 5.8422 30 0.33 175 0.461 4.9170 9.2683 5.0392 0.9377 30 0.483 5.1614 9.4867 40 0.37 200 0.539 5.7836 10.033

5.8225 0.1040 40 0.546 5.8614 10.046 50 0.39 235 0.560 5.9486 13.632

6.0041 1.3686 50 0.670 6.0597 13.741


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Table 12: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Lexan Polycarbonate + 20% SGF / C120 steel at a sliding speed of27.85 cm/s.

N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

20 0.33 200 3.9390 0.5142 20 0.363 3.9057 5.1255 30 0.40 240 0.369 3.9724 5.1595 4.3696 0.8153 30 0.408 4.3419 8.1472 40 0.42 250 0.413 4.3974 8.1982 4.9169 1.1594

Table 13: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Lexan Polycarbonate + 20% SGF / C120 steel at a sliding speed of37.13 cm/s.

N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

20 0.30 150 0.415 4.4835 5.4740 4.3668 0.5406 20 0.394 4.2501 5.3380 30 0.33 175 0.464 4.9641 8.6827 4.9807 0.8702 30 0.467 4.9974 8.7210 40 0.37 200 0.526 5.5781 12.325

5.6225 1.2367 40 0.533 5.5667 12.410 50 0.39 235 0.600 6.3476 15.810

6.3643 1.6150 50 0.603 0.6810 18.490

Table 14: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Lexan Polycarbonate + 20% SGF / C120 steel at a sliding speed of 46.41 cm/s.

N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

10 0.37 220 0.366 4.0028 2.5712 4.0361 0.2582 10 0.372 4.0695 1.5925 20 0.41 249 0.430 4.6501 5.5760 4.6723 0.5589 20 0.434 4.6946 5.6015 30 0.42 260 0.506 5.4308 9.0652

5.4419 0.9078 30 0.508 5.4530 9.0907 40 0.44 270 0.589 6.2892 13.039

6.3357 1.3090 40 0.366 4.0028 2.5712


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Table 15: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Noryl Polyamide + 20% SGF / C120 steel at a sliding speed of 46.41 cm/s.

N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

20 0.27 150 0.303 3.2470 4.3915 3.2692 0.4403 20 0.307 3.2915 4.4154 30 0.28 165 0.357 3.7274 9.5162 3.7441 0.9540 30 0.360 3.7608 9.5640 40 0.31 180 0.472 3.8856 16.426

4.9134 1.6462 40 0.477 4.9412 16.498 50 0.33 220 0.610 6.2993 24.898

6.3271 2.4946 50 0.615 6.3549 24.994

Table 16: Results of the experimental tests carried out to determine the wear and wear rate of the metal sample. The friction couple: Noryl Polyamide + 20% SGF / C120 steel at a sliding speed of 55.70 cm/s.

N (N)



lm2

(mm2) hu (10-4 mm)

Vu

(10-4 mm3)


Vmu (10-6 cm3 /h)

20 0.29 160 0.416 4.3830 10.281 4.3885 1.0289 20 0.417 4.3941 10.297 30 0.32 175 0.476 4.9300 16.498 4.9133 1.6474 30 0.473 4.8967 16.450 40 0.34 185 0.643 6.6660 25.568

6.6604 2.5552 40 0.642 6.6549 25.536 50 0.36 230 0.766 7.9131 34.869

7.8853 3.4829 50 0.761 7.8575 34.789

As example, the authors consider processing measured data (Table 1), and also an

exemplification of the presentation qualitatively-quantitatively graphics (Figure 3). That's why a suggestive graphical representation was sought, to provide a qualitative

correlation between the two sizes that relates them to the contact temperature and based on which to determine a quantitative correlation – Figure4.

It is well known the law established by Coulomb (1780) that the friction force Ff is direct proportional to the normal force N:

NF f (2)

More studies conducted later have shown that , the friction coefficient, is not only dependent

on the normal force (Capitanu et al., 2015). Relations for variations of the friction force, depending on the applied load can be considered of the form:


91

n

f bNaNF (3)

or more simply

bNaF f (4)

or:

n

f bNaF (5)

(a)

(b)

Figure 3: The variation of wear volume (a) in 10-6 cm3/h, wear depth (b) in 10-4 mm/h and contact temperature in 0C of the C120 steel surface, in linear dry sliding contact with polyamide Nylonplast AVE with 30% SGF, at the sliding speed of 18.56 cm/s, depending on the normal load (contact pressure) applied.


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Figure 4: Qualitative evolution of the wear scar of steel surface in linear contact dry friction with polyamide Nylonplast AVE with 30% SGF depending on the normal load (contact pressure) applied, at the sliding speed of 18.56 cm/s. Contact temperature in 0C.

Last relationships lead to the conclusion that when the normal force is equal to 0, the friction

force has other value than 0 ( aF f ). Although this could be explained by the presence of a

remanent force of adhesion of the two surfaces, even after the removal of the normal load, however, the authors consider more accurate the use of a relationship of the form:

n

f kNF (6)

Where n is sub-unitary.

Friction coefficient, according to Coulomb's Law, has the expression (Eq. 2) NF f / .The

friction coefficient for the plastic materials can be expressed and in the following form:

cf p/ (7)

where f represents the shear strength of the softer material, and cp represents the flow

pressure of the same material. Because 3/HBpc , results:

HBf /3 (8)

Equation (7) is in agreement with the experimental preliminary results.


93

All the variation curves of the output parameter of the frictional system (amount of wear, wear depth, friction coefficient, contact temperature) depending on input parameters - normal load (contact pressure), the sliding speed while maintaining the steady state surface (roughness Ra), show a strong nonlinearity due to the behaviour of the elastic - plastic polymers tested. In this situation, the authors tried an approach to metal surface wear by ANN because of its ability to model very complex and strongly nonlinear phenomena. This was the qualitative - quantitative analytical approach previously achieved. Next, only the tables with the other experimental data obtained are presented, without the analytical approach, previously exemplified in Table 1 and Figures 3 and 4. The analytic and graphic processing of these results was presented elsewhere – (Rus et al., 2014).

Wear processes involve very complex and powerfully nonlinear phenomena. Analytic models are difficult or impossible to obtain, are necessary the multiple inputs - contact pressure, relative sliding speed, measured contact temperature, materials properties and outputs - width and depth of the wear scar, measured contact temperature, which influence each other continually. The paper aims to use the same experimental data in an ANN – based approach, which is a state-of-the-art modelling method, due to its properties for learning, generalisation and nonlinear behaviour, adequate to plastic materials armed with short glass fibres. The innovative approach is compared with a baseline model featuring multivariate linear regression optimised using gradient descent.

In the next section, the authors refer to the ANN's steel surface wear approach and regression models in the case linear dry contact of plastics reinforced with short glass fibres (SGF) on C120 and Rp3 steel, under the same experimental conditions.

3.0 APPROACHING METTALLIC SURFACE WEAR THROUGH ANN AND REGRESSION MODELS

The data was obtained through experiments run on friction couples with linear contact using three different types of polymers on two different types of steel variants. Aside from alternating the materials used, the speed and pressure applied to them were varied under the same operating conditions. This was done with regard to the particulars of each material combination and levels of speed and pressure. The resulting dataset includes the information from Table 17.

The current dataset may contain outliers as with any data obtained from experimental setups. These are inadequate values usually resulting from experimental error or laboratory unforeseen circumstances. Outliers can influence the entire process, so they need to be eliminated from the dataset. This can usually be accomplished satisfactorily by applying a simple data filter (e.g. distance to median).

The first model considered is a multivariate linear regression. The first step in a multiple variable regression model is to normalize the features and then run a batch gradient descent algorithm on the data, where each iteration minimizes the cost function by simultaneously updating all θ parameters. The linear regression model also includes regularization factors to prevent over-fitting. The regularization component is included in the cost function and provides a penalty for the data being fitted too closely using the polynomial variables.


94

Table 17: Types of variables. Variable Modelled Type Range Unit Observations

Material Independent

Categorical - Nominal

N/A N/A The material may be treated as a nominal variable, or as continuous variable(s) by taking into account the specific properties of the mix.

Continuous - -

Speed Independent Continuous 18.56 – 153.55

cm/s Max. 7 levels per material type.

Pressure Independent Continuous 10 - 50 N Max. 4 levels per material type and speed.

Friction Coefficient

Dependent Continuous 0.26 – 0.5 -

Modelled as a function of material, speed, pressure. Second application.

Contact Temperature

Dependent Continuous 98 - 300 0C

Modelled as a function of material, speed, pressure. Second application.

Wear depth Dependent Continuous 0.9 – 9.1 10-

4mm3

Modelled as a function of material, speed, pressure. Both applications.

Wear volume Dependent Continuous 0.13 – 3.48

10-4 mm3

Modelled as a function of material, speed, pressure. Both applications.

The optimisation problem is described as 𝑌 = 𝜃 ∗ 𝑋, where X is the input data, namely the

three dependent variables, containing all data-points, plus an intercept term. Y is the output data, alternatively the wear speed, wear volume, friction coefficient or friction temperature, that the algorithm is trying to learn, and θ is the matrix of parameters used to estimate Y from X. The challenge is finding the best θ which minimizes the error between the actual Y and the estimate. This is obtained from �̂� = 𝜃𝐿𝑅 ∗ 𝑋, or, in extended form:

[ 𝑦1̂

𝑦2̂

𝑦3̂

⋮𝑦�̂�]

=

[ 11

⋯ 1(𝑚+1)

⋮ ⋱ ⋮

𝑛1

⋯ 𝑛(𝑚+1)]

∗

[ 𝑥1

𝑥2

⋮𝑥𝑚

𝑖𝑛𝑡]

(9)


95

There will be m features and an intercept term, which helps prevent over-fitting. The total sum of all errors, across all values, is defined as the cost function J. It is this cost function that the optimisation algorithms attempt to minimise.

Gradient descent is an optimization algorithm where the potential solution is improved each iteration by moving along the feature gradient in the variable space.

While it requires that the target function be differentiable and it is somewhat susceptible to local minima, gradient descent provides a stable and computationally inexpensive algorithm for function optimization.

Neural networks work by solving for the best dynamic weights of a hidden layer of neurons, which determine the strength with which these are fired. While solving for a linear or polynomial regression model provides an explicit relation between dependent and independent variables, it may be that an implicit representation model, such as a neural network, would yield better results.

The code for the various optimisations was developed in Octave for plotting end most of the fitting problems, while Matlab was used for the graphical neural network tool. While the figures provide a good overview of the models’ behaviour, they fail to give an analytical measure of model performance.

For this, two metrics are used, both of which give a numerical measure of the error: the mean square error (MSE) and the mean absolute error (MAE). Since these are metrics for the error of the model, lower values correlate to better performance. The mathematical expressions are shown below:

𝑀𝑆𝐸 =1

𝑛∑ (𝑋𝑖 ∗ 𝜃 − 𝑌𝑖)

2

𝑖=1..𝑛

(10)

𝑀𝐴𝐸 =1

𝑛∑ |𝑋𝑖 ∗ 𝜃 − 𝑌𝑖|

𝑖=1..𝑛

(11)

The approach is divided into two applications, whereby the first application takes the wear

depth and wear volume as dependent on speed and pressure, without considering the material differences, and the second application investigates the wear depth, wear volume, friction coefficient and temperature as dependent variables upon speed, pressure and eight material characteristics.

3.1 The Bivariate Learning Application

The first step is to plot the available data and pre-process any necessary alterations. For the first dependent variable group, the data points resulting from running the experiment with a speed of above 60 cm/s were eliminated, since those were only relevant for a minority of the obtained samples. The outliers can also be identified plotting the data, as can be seen in Figures5 and 6, some data points, marked in red, are noticeably removed from the main cloud of points. In this particular case, it is not a matter of errant experimental data, but rather the result of running the tests with higher speeds only on very few occasions. Still, their exclusion is indicated, in order to better concentrate the algorithm on a dense cloud of points – the remaining ones, in blue. After eliminating the outliers, there are 52 useful samples left for the learning algorithm to be run on.


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The resulting dataset is then used to train a linear regression model for each of the two considered dependent variables: wear depth and wear volume. This model assumes the dependent variables to be a linear combination of the considered independent variables, speed and pressure, and an intercept term, which does not vary with the independent variables. The intercept term is added only for the linear regression problem, since the neural network algorithm will do the same on its own.

The optimisation problem is then to find the best coefficients (thetas) that minimise the cost function (J), which gives a measurement of the difference between the empirical values of the two dependent variables and their estimates obtained through linear regression. Gradient descent is the algorithm used to iteratively arrive at the best possible set of thetas. The learning rate, lambda, is set to 1.

Figure 5: Wear depth experimental data in 10-4 mm/h with highlighted outliers.

Figure 6: Wear volume experimental data in 10-6 cm3/h with highlighted outliers.


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The first series of tests do not make use of the material as a numerical value. The model becomes

�̂�52𝑥1 = [𝑉52𝑥1𝑁52𝑥1152𝑥1]52𝑥3 ∗ 𝜃3𝑥1, (12) Where is the speed and N is the pressure. In extended form, for the i-th sample of a variable, this means that �̂�𝑖 = 𝜃1 ∗ 𝑉𝑖 + 𝜃2 ∗ 𝑁𝑖 + 𝜃3, where y can be either the wear depth or wear volume, as the two dependent variables are treated separately, both according to this model. This will of course yield different sets of Θ for each.

Finally, after plotting, pre-processing the data and adding the intercept term, the linear regression algorithm is run using a standard gradient function, limited to 400 iterations. The resulting thetas are:

𝜃ℎ = [0.01290.06170.0855

]and 𝜃𝑣𝑜𝑙 = [−0.74650.01380.0416

],

(13)

meaning that the prediction model becomes:

{ ℎ̂ = 0.0129 ∗ 𝑉 + 0.0617 ∗ 𝑁 + 0.0855𝑣𝑜�̂� = −0.7465 ∗ 𝑉 + 0.0138 ∗ 𝑁 + 0.0416

(14)

The second model is a neural network with one hidden layer consisting of 25 hidden neurons.

The network is trained on the same data using two training algorithms: Levenberg - Marquardt and Bayesian regularization. The best resulting network, judged by mean square error and correlation factor, is saved as a prediction function which takes in the independent variable values and outputs values for the two dependent variables. As usual with neural networks, the available date is split into training (70%), cross-validation (15%) and testing (15%). In the case of the present dataset, this works out to 36 samples for training and 8 each for validation and testing.

Figures 7, 8 and 9, 10 show the plotted fit for the available data, using the two methods, for wear depth and wear volume, respectively.

Figure 7: Linear regression fit for wear depth in 10-4 mm/h.


98

Figure 8: Neural network fit for wear depth in 10-4mm/h.

Figure 9: Linear regression fit for wear volume in 10-6 cm3/h.

Figure 10: Neural network fit for wear volume in 10-6 cm3/h.


99

For the first optimisation problem, which models the wear depth and volume dependent on speed and pressure, the metric results are shown in the Table 18 below.

Table 18: The wear depth and volume models dependent on speed and pressure.

Wear Depth Wear Volume MSE MAE MSE MAE

Linear Regression 0.3798 0.4515 0.1479 0.2361 Neural Network 0.3791 0.4246 0.1025 0.1720

As can be seen from the table, the neural network model outperforms linear regression across

the board. However, both models show very good performance, which is to be expected for this initial simplified problem.

3.2 The Multivariate Learning Application

The second series of tests uses numerical characteristics of the material to introduce additional independent variables into the model. The chosen variables have a full complement of values for each of the materials used in the experiment. The relevant values are shown in the Tables 19 and 20 below.

Table19: Numerical characteristics of the plastic materials reinforced with SGF to introduce additional independent variables into the model.

Polyamide Specific Weight

Water Absorption

Elasticity Thermal Conductivity

Linear Dilation

Nylonplast AVE 1.35 0.8 80 0.34 3.3 Noryl 1.27 0.06 84 0.196 2.5 Lexan 1.35 0.16 86 0.5 2.68

Table 20: Numerical characteristics of the steels to introduce additional independent variables into the model.

Rp 3 steel C Si Mn

max S max

P max

Cr Mo V Ni max

W

0.7-0.8 0.2-0.4 0.45 0.02 0.025 3.5-4.4 0.6 1.0-1.4 0.4 17.5-19.5 C120 steel

C Si Mn S max

P max

Cr Mo V Ni max

W

1.8-2.2 0.15-0.35 0.15-0.45 0.025 0.03 11-33 - - 0.35 -

The new model adds 8 new independent variables, obtained from the material properties. Including the intercept term, the model now becomes �̂�52𝑥1 = 𝑋52𝑥11 ∗ 𝜃11𝑥1. Figures 11 and 12 show the plotted data. Because of the increased dimensionality, the data cannot be plotted as a graph dependent on the independent variables. Therefore, a two-dimensional graph based on the index was chosen instead. For the same reason, the data now has no discernible outliers, as can be seen in the figure, so all pre-processing conditions were eliminated.


100

Figure 11: Experimental data for second series of tests on wear depth in 10-4mm/h.

Figure 12: Experimental data for second series of tests on wear volume in 10-6 cm3/h.

For this particular dataset, there are more data available when considering two of the

dependent variables, wear depth and volume, than the other two, friction coefficient and temperature. This is because measurements are more easily made for the former than the latter, meaning some data points are incomplete in those fields. When considering solely depth and volume, some outliers were eliminated in order to obtain a smoother process. This is an improvement not afforded to the second group of variables, since it would leave the algorithms with too few data points to work on. Therefore, in order to treat both groups concurrently, only those samples with complete information were considered. This leaves 45samples to be worked on by the learning algorithms.

After running the linear regression algorithm, the resulting thetas are presented in Table 21.

Table 21: Linear regression coefficients. Θh Θvol Θu ΘT

Intercept 0.069 3.1970 0.0021 -626.7381 Speed 0.0301 0.0022 0.0005 1.1245 Pressure 0.0968 0.0365 0.004 2.4632 Specific Weight 0.0288 -0.076 0.0074 4.0941 Water Absorption 0.0574 -0.2432 0.0265 12.0803 Elasticity 0.0078 -0.0259 0.0018 7.8152 Thermal Conductivity 0.1514 -0.313 0.0404 17.5419 Linear Dilation 0.0716 -0.3015 0.0166 15.1130 S max 0.0288 0.0074 0.0021 -0.3950 P max 0.0276 0.0062 0.0009 -0.5111 Ni max -0.2827 -0.0539 -0.0132 4.6144


101

For each dependent variable, the prediction is a dot-product of the independent variable values and its respective theta vector. The linear regression coefficients show the relative influence a certain independent variable has on the prediction of a dependent variable. The intercept term is a baseline starting point for the prediction and models and aggregation of all other factors not considered and the inherent randomness of the model.

There are two possible approaches to the neural network model for this multiple input multiple output problem, both of which are investigated in the paper. The first is to train a neural network independently for each of the four dependent variables. These networks will again consist of a hidden layer with 25 hidden neurons. The second possibility is to train a single neural network for the entire problem, with a hidden layer of 100 neurons. The increased number is selected to allow the network flexibility to learn all four dependent variables concurrently.

All selected networks were trained using the Bayesian regularization algorithm. Figures 13 - 20 show the model fit of the data, again using per-index representations.

Figure 13: Linear regression fit for wear depth in 10-4mm/h.

Figure 14: Neural network fit for wear depth in 10-4mm/h.


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Figure 15: Linear regression fit for wear volume in 10-6 cm3/h.

Figure 16: Neural network fit for wear volume in 10-6 cm3/h.

Figure 17: Linear regression fit for friction coefficient.

Figure 18: Neural network fit for friction coefficient.


103

Figure 19: Linear regression fit for temperature in 0C.

Figure 20: Neural network fit for temperature in 0C.

For the second, more complex, optimisation problem, which models the wear depth, volume,

friction coefficient and temperature dependent on speed, pressure and eight material characteristics, the metric results are shown in the Table 22 below.

Table 22: Metric results the wear depth and volume models dependent on speed, pressure and eight material characteristics.

Wear Depth Wear Volume Friction Coefficient

Temperature

MSE MAE MSE MAE MSE MAE MSE MAE Linear Regression

0.5451 0.5454 0.0740 0.1593 0.0028 0.0444 1262.4 24.93

Neural Network

0.0699 0.1982 0.0244 0.0526 0.0024 0.039 1312.3 22.52

Large Neural Network

2.3165

1.2412

0.4229

0.5609

0.005

0.0613

909.04

19.61

As can be seen from the table, the single-output neural networks clearly and significantly

outperform linear regression for all metrics in the second series. This is because of the far more non-linear behaviour of the data set, as opposed to the first series, which makes it more difficult for a linear model to obtain a good fit of the data. The multi-output neural network fares worse in every category, save for the dependent variable of temperature. This is because it strives to find


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the best possible solution for predicting all the dependent variables at once. Based on the very non-linear nature of the last dependent variable, the optimum found makes significant concessions in the performance for the other three variables.

The superior performance of the individual neural networks is clear both in the metrics and even in the visual plots. It is these functions that will be further improved through the addition of more data, as it becomes available, and will be used to predict the future behaviour of the experiment. 4.0 CONCLUSIONS

This paper presents the proposed methods, models and algorithms for obtaining a relation, be it explicit or implicit, between various variables of interest found in the tribological process. To that end, a number of options were explored for each tier of the overall modelling process. Of particular regard were methods relating to how the data is obtained, screened and pre-processed, the models taken under consideration, and the various possible optimisation algorithms employed to achieve the best fit of the existing data to the chosen model.

The first application is chosen to be a simpler learning problem investigating the relation between two dependent variables (wear depth and volume) and two independent variables (speed and pressure), useful for testing out assumptions and illustrating the possibilities of the model. The second application makes full use of the data set, considering four dependent variables upon ten independent variables and three possible learning models – multivariate regression, individual neural networks (25 neurons each) and a single large neural network of 100 hidden neurons. For each application, two cost functions are calculated, which form the basis of the results and discussion.

Of course, most of the available possibilities for the fitting of data-intensive models, resulting in complex optimisation problems, are heuristic algorithms. The fitting problem itself is of the nature that there is always an error present, which needs to be minimised. It should also be noted that correlation does not imply causality and it is up to the investigator to ensure that the correct conclusions are drawn from the resulting design. This does not invalidate the model, as the prediction algorithm is still valid in a similar context.

The results show significantly better performance across all norms for the neural network algorithm, which was to be expected. Even so, the obtained prediction function provides a good fit of the model, with little error and no over-fitting, as can be concluded from the testing phase of the algorithm. Once trained, the predictive model can be used instead of the actual analytical approach in any application where the dependent variables are needed and the independent variable values are available, within a similar context. This reduces the mathematical complexity of the overall application and could find use in a range of computationally intensive models.

Because wear processes are complex phenomena and their analytical models are difficult or impossible to obtain (are powerfully nonlinear and require multiple inputs), the authors have developed, based on the ANN model, an innovative modelling method that has an optimized multivariate linear regression using gradient descent.

Further directions of research include substituting gradient descent with more advanced evolutionary algorithms, such as genetic algorithms or particle swarm optimisation, for the baseline regression analysis, as well as more variations in the type and depth or the neural networks used, as more data become available. New datasets will be obtained from similar tribological processes, which may allow more generalised models to be fitted to the same wear


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diagnosis problem. The application of these and future results obtained from continuing research on this topic will lead to better, more robust applications in prosthesis design and automated control [30,31], as well as the field of tribology at large. ACKNOWLEDGEMENT

This work was supported by a grant of the Romanian Ministry of Research and Innovation, CCCDI-UEFISCDI, MULTIMOND2 project number PN-III-P1-1.2-PCCDI2017-0637/33PCCDI/01.03.2018, and by KEYTHROB project, number PN-III-P3-3.1-PM-RO-CN-2018-0144 / 2 BM ⁄ 2018, within PNCDI III, and by the European Commission Marie Skłodowska-Curie SMOOTH project, Smart Robots for Fire-Fighting, H2020-MSCA-RISE-2016-734875.

The authors gratefully acknowledge the financial support of Department of Technical Sciences of the Romanian Academy. REFERENCES Abouelatta, O. B. (2013). Prediction of machining operations and surface roughness using artificial

neural network. J. Eng. Sci, 41(3), 1021-1044. Al-Zubaidi, S., Ghani, J. A., & Haron, C. H. C. (2013). Prediction of surface roughness when end

milling Ti6Al4V alloy using adaptive neurofuzzy inference system. Modelling and Simulation in Engineering, 2013, 10.

Capitanu, L., Rus, D., Florescu, V. (2014). A qualitative-quantitative correlation of friction and wear processes of steel surfaces in linear dry contact with SGF. In Proceedings of Balkantrib’14 - 8th International Conference on Tribology, pp.611-623.

Capitanu, L., Vladareanu, L., & Florescu, V. (2015). The Knee Wear Prediction of UHMWPE Tibial Insert Using VIPRO Platform. Infinite Study.

Capitanu, L., Vladareanu, L., Onisoru, J., Iarovici, A., Tiganesteanu, C., & Dima, M. (2008). Mathematical model and artificial knee joints wear control. Journal of the Balkan Tribological Association, 14(1), 87-101.

Chen, J.C., Savage, M. (2001). A fuzzy-net-based multilevel in-process surface roughness recognition system in milling operations. The International Journal of Advanced Manufacturing Technology, 17(9), 670–676.

Evans, D. C., & Lancaster, J. K. (1979). The wear of polymers. In Treatise on Materials Science & Technology (Vol. 13, pp. 85-139). Elsevier.

Fadare, D. A., Ezugwu, E. O., & Bonney, J. (2009). Intelligent tool condition monitoring in high-speed turning of Titanium Ti-6Al-4V alloy. Journal of Science and Technology (Ghana), 29(3).

Feng, C. X. J., Wang, X. D., Yu, Z. S. (2002). Neural networks modelling of honing surface roughness parameters defined by ISO13565. Journal of Manufacturing Systems, 21(5), 395-408.

Feng, Chang-Xue Jack, Zhi-Guang Yu, and Andrew Kusiak. "Selection and validation of predictive regression and neural network models based on designed experiments." IIE Transactions 38, no. 1 (2006): 13-23.

Flepp, B. (1999). Wear diagnosis of mechanical seals with neural networks (Doctoral dissertation, ETH Zurich).

Friedrich, K., Akpan, E., & Wetzel, B. (2018). Sliding wear performance of dry and oil impregnated black-fiber palm wood. JURNAL TRIBOLOGI, 16, 51-70.


106

Jumahat, A., Kasolang, S., & Bahari, M. T. (2015). Wear properties of nanosilica filled epoxy polymers and FRP composites. Jurnal Tribologi, 6, 24-36.

Kalidass, S., Palanisamy, P., & Muthukumaran, V. (2012). Prediction of tool wear using regression and artificial neural network models in end milling of AISI 304 austenitic stainless steel. International Journal of Engineering and Innovative Technology, 1(2), 29-35.

Liu, J., Xu, C., Jackson, M. (2011). Traditional and non-traditional control techniques for grinding processes. In Mark J. Jackson, J. Paulo Davim, Machining with Abrasives. Springer, New York Dordrecht Heidelberg London, 269-302.

Mak, C. W., Afzulpurkar, N. V., Dailey, M. N., & Saram, P. B. (2014). A Bayesian approach to automated optical inspection for solder jet ball joint defects in the head gimbal assembly process. IEEE Transactions on Automation Science and Engineering, 11(4), 1155-1162.

Mcleay, T., & Turner, M. S. (2011). Failure mode analysis to define process monitoring systems. Journal of machine engineering, 11(4), 118-129.

Mohmad, M., Abdollah, M. F. B., Khudhair, A. Q., Tamaldin, N., Amiruddin, H., Zin, M. R. B. M., & Tunggal, D. (2018). Physical-mechanical properties of palm kernel activated carbon reinforced polymeric composite: Potential as a self-lubricating material. Jurnal Tribologi, 17, 77-92.

Nasir, R. M., & Ghazali, N. M. (2014). Tribological performance of paddy straw reinforced polypropylene (PSRP) and unidirectional glass-pultruded-kenaf (UGPK) composites. Jurnal Tribologi, 1, 1-17.

Panda, S. S., Singh, A. K., Chakraborty, D., & Pal, S. K. (2006). Drill wear monitoring using back propagation neural network. Journal of Materials Processing Technology, 172(2), 283-290.

Pati, P.R., Satapathy, A. (2013). Prediction and simulation of erosion wear response of Linz-Donawitz (LD) slag filled epoxy composites using ANN. International Journal on Mechanical Engineering and Robotics (IJMER), 1(1), 39-45.

Rao B.K.N, SrinivasaPai, P., Nagabhushana, T.N. (2012). Failure diagnosis and prognosis of rolling – element bearings using artificial neural networks: A critical overview. Journal of Physics: Conference Series, 364, 012023.

Rao, K. S., Varadarajan, Y. S., Rajendra, N. (2014). Artificial neural approach for the prediction of abrasive wear behavior of carbon fabric reinforced epoxy composite. Indian Journal of Engineering & Materials Sciences, 21, 16-22.

Ripa, M., & Frangu, L. (2004). A survey of artificial neural networks applications in wear and manufacturing processes. Journal of Tribology, 35-42.

Rus, D., Capitanu, L., & Badita, L. L. (2014). A qualitative correlation between friction coefficient and steel surface wear in linear dry sliding contact to polymers with SGF. Friction, 2(1), 47-57.

Shebani, A., & Pislaru, C. (2015). Wear measuring and wear modelling based on Archard, ASTM, and neural network models. International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering, 9(1), 177-182.

Shukla, R. K. (2006). Applications of artificial neural networks in manufacturing: An overview. In Proceedings of the National Conference on Trends and Advances in Mechanical Engineering, YMCA Institute of Engineering, Faridabad, Haryana, 5 pages.

Velasco, F. J. M. (2012). A Bayesian Network approach to diagnosing the root cause of failure from Trouble Tickets. Artif. Intell. Research, 1(2), 75-85.


107

Vladareanu, L., Iliescu, M., Wang, H., Yongfei, F., Vladareanu, V., Yu, H., Smarandache, F. (2017). CSP and 'omics' technology applied on versatile and intelligent portable platform, International Conference on Advanced Mechatronic Systems, ICAMechS 7813485, 423-428.

Vladareanu, L., Ion, I., Velea, L. M., Mitroi, D. (2009). The robot hybrid position and force control in multi-microprocessor systems. WSEAS Transactions on Systems, 8(1), 148-157.

Vladareanu, L., Tont, G., Ion, I., Gal, A., Melinte, O. (2010). Fuzzy dynamic modeling for walking modular robot control. Proceedings of the 9th International Conference on Applications of Electrical Engineering, AEE '10, 163-170.

Vladareanu, V., Capitanu, L., Vladareanu, V. (2018). Neuro-Fuzzy modelling of the metallic surface characterization on linear dry contact between plastic material reinforced with SGF and alloyed steel, Materials, 11(7), 1181 -1202.

Vladareanu, V., Dumitrache, I., Vladareanu, L., Sacala, I. S., Tont , G., Moisescu, M. A. (2015). Versatile intelligent portable robot control platform based on cyber physical systems principles. Studies in Informatics and Control, 24(4), 409-418.

Wang, L., Chan, C. Y. (2012). Establishment of low-cost production monitoring technique. In Proceedings of the World Congress on Engineering, Vol III, WCE 2012, 4 pages.

Willert, H. G., Semlitsch, M. (1977). Reactions of the articular capsule to wear products of artificial joint prostheses. Journal of Biomedical Materials Research, 11(2), 157-164.

Zhang, Z., Barkoula, N. M., Karger-Kocsis, J., & Friedrich, K. (2003). Artificial neural network predictions on erosive wear of polymers. Wear, 255(1), 708-713.

a neural network approach to the steel surface wear on

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